Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation

Journal Article · Wed Jul 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4927249· OSTI ID:22479580

Mi, Lufang ^[1]; Cong, Hongzi ^[2]

---

1. Department of Mathematics, Binzhou University, Shandong 256600 (China)
2. School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024 (China)

In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small ε, there is a large subset S′ of S such that for all s ∈ S′, the solution u of the unperturbed system persists as a time-quasi-periodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients.

• OSTI ID: 22479580
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
EQUATIONS
LYAPUNOV METHOD
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PERIODICITY
PERTURBATION THEORY
POTENTIALS